# Is it true that real world data is highly discontinuous?

A function $$f$$ is said to be continuous at a point $$c$$ if it satisfies three properties:

1. Should be defined at the point $$c$$
2. Left and right-hand limits at $$c$$ must be equal i.e., the limit must exist
3. Limit value at point $$c$$ is equal to the actual value of the function at c

In short: $$\lim \limits_{x \rightarrow c} f(x) = f(c)$$

I want to know whether the functions that we want to learn through real-world data, say generator in GAN, such as images, audio, video, text corpora, etc., are continuous or highly discontinuous in general? If discontinuous, what might be the reason for discontinuity? I mean, which among the three properties mentioned got a violation in the majority of cases?

• As said in the description, discontinuity is a property of the function. So, we can't talk of it just by looking at the data. It all depends on what kind of function to define over it. Aug 22 '21 at 1:41
• @SpiderRico I mean suppose I want to learn a generator, Then the function is the function of generator neural network... Aug 22 '21 at 1:45
• @SpiderRico so are you saying to narrow down the function I want to simulate? Aug 22 '21 at 1:46